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Expanding means multiplying out brackets so an expression has no brackets left. It is the reverse of factorising and shows up everywhere — from solving equations to differentiating. The golden rule never changes: every term inside must be multiplied by every term outside.
What you'll be able to do
To expand a single bracket, multiply the term outside by term inside. Watch the signs carefully — a negative outside the bracket flips the sign of everything inside.
Tip — A negative sign outside the bracket is a multiplier of −1. Treat it like any other factor and the signs take care of themselves.
For two brackets, every term in the first must multiply every term in the second — four products in total. A common memory aid is : First, Outer, Inner, Last. A grid (box) method does exactly the same job and is harder to rush.
Tip — Always combine the two “middle” terms. Leaving them separate is the single most common expanding error.
Squaring a bracket is just expanding it by itself. The shortcut saves time, but only if you remember the middle term.
The “difference of two squares” pattern is worth memorising too: the middle terms cancel.
Tip — is NOT . The cross terms give the in the middle.
With three brackets, expand of them first, then multiply the result by the third bracket. Keep your work neat and collect like terms only at the very end.
Tip — It does not matter which two brackets you expand first — pick the pair that looks easiest.
Formula recap
Common mistakes to avoid
Key takeaways
Test yourself
Ready to lock in Expanding Brackets? Pick a mode and earn XP & Dobloons.